Fat-fractal scaling exponent of area-preserving maps
- 1 February 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 35 (3) , 1470-1473
- https://doi.org/10.1103/physreva.35.1470
Abstract
An upper bound for the fat-fractal scaling exponent of area-preserving maps is calculated. The calculation consists of counting the number of islands of different sizes that occur near a Kolmogorov-Arnol’d-Moser surface. Approximate renormalization scaling results are used for the island sizes and numbers.Keywords
This publication has 14 references indexed in Scilit:
- Characterization of Fat Fractals in Nonlinear Dynamical SystemsPhysical Review Letters, 1986
- Farmer and Umberger respondPhysical Review Letters, 1986
- Comment on ‘‘Sensitive dependence on parameters in nonlinear dynamics’’ and on ‘‘Fat fractals on the energy surface’’Physical Review Letters, 1986
- Fat Fractals on the Energy SurfacePhysical Review Letters, 1985
- Sensitive dependence on parameters in nonlinear dynamicsPhysical Review Letters, 1985
- Exterior dimension of fat fractalsPhysics Letters A, 1985
- A renormalization approach to invariant circles in area-preserving mapsPhysica D: Nonlinear Phenomena, 1983
- Regular and Stochastic MotionPublished by Springer Nature ,1983
- Critical behavior of a KAM surface: I. Empirical resultsJournal of Statistical Physics, 1982
- Scaling for a Critical Kolmogorov-Arnold-Moser TrajectoryPhysical Review Letters, 1981